Routing Channel-Patch Dependencies in Time Series Forecasting with Graph Spectral Decomposition

Multivariate time-series analysis involves extracting informative representations from sequences of multiple interdependent variables, supporting tasks such as forecasting, imputation, and anomaly detection. In real-world scenarios, these variables are typically collected from a shared context or underlying phenomenon, suggesting the presence of latent dependencies across time and channels that can be leveraged to improve performance. However, recent findings show that channel-independent (CI) models, which assume no inter-variable dependencies, often outperform channel-dependent (CD) models that explicitly model such relationships. This surprising result indicates that current CD models may not fully exploit their potential due to limitations in how dependencies are captured. Recent studies have revisited channel dependence modeling with various approaches; however, these methods often employ indirect modeling strategies, which can lead to meaningful dependencies being overlooked. To address this issue, we introduce XCTFormer, a transformer-based channel-dependent (CD) model that explicitly captures cross-temporal and cross-channel dependencies via an enhanced attention mechanism. The model operates in a token-to-token fashion, modeling pairwise dependencies between every pair of tokens across time and channels. The architecture comprises (i) a data processing module, (ii) a novel Cross-Relational Attention Block (CRAB) that increases capacity and expressiveness, and (iii) an optional Dependency Compression Plugin (DeCoP) that improves scalability. Through extensive experiments on three time-series benchmarks, we show that XCTFormer achieves strong results compared to widely recognized baselines; in particular, it attains state-of-the-art performance on the imputation task, outperforming the second-best method by an average of 20.8% in MSE and 15.3% in MAE.

Multivariate time series forecasting plays a critical role in real-world applications, including weather prediction, stock analysis, and health monitoring. Due to the diversity of data sources, time series exhibit diverse temporal dynamics, often accompanied by various irregularities such as missing values and non-uniform sampling frequencies. Such irregularities lead to complex and asynchronous temporal dependencies across channels. Thus, a single model with a fixed patching scheme often fails to adapt well to diverse multivariate time series, hindering accurate forecasting. In this paper, we propose TiWeaver, a unified framework designed to handle temporal dynamics and fine-grained inter-channel dependencies adaptively. Specifically, we introduce a Graph-Guided Adaptive Tokenizer (G$^2$AT) that divides time series into high contextually coherent patches by jointly considering temporal density and representation consistency. In addition, we propose a Fine-grained Asynchronous Dependency Extractor (FADE), which is designed to model fine-grained asynchronous inter-channel dependencies while incorporating long-term historical dependencies. We evaluate TiWeaver on 12 real-world time series datasets, where it achieves state-of-the-art performance, outperforming existing methods up to 25%. These results demonstrate its robustness and effectiveness across diverse domains and data characteristics.

Multivariate time series forecasting often struggles to capture long-range dependencies due to fixed lookback windows. Retrieval-augmented forecasting addresses this by retrieving historical segments from memory, but existing approaches rely on a channel-agnostic strategy that applies the same references to all variables. This neglects inter-variable heterogeneity, where different channels exhibit distinct periodicities and spectral profiles. We propose CRAFT (Channel-wise retrieval-augmented forecasting), a novel framework that performs retrieval independently for each channel. To ensure efficiency, CRAFT adopts a two-stage pipeline: a sparse relation graph constructed in the time domain prunes irrelevant candidates, and spectral similarity in the frequency domain ranks references, emphasizing dominant periodic components while suppressing noise. Experiments on seven public benchmarks demonstrate that CRAFT outperforms state-of-the-art forecasting baselines, achieving superior accuracy with practical inference efficiency.